Edwards began his career on radio, as creator, writer, and later director of the tongue-in-cheek series Richard Diamond, Private Detective, from 1949 until 1952. He later worked on the TV series Peter Gunn. His other film credits include Breakfast at Tiffany's, Operation Petticoat (with Cary Grant), The Great Race (with Jack Lemmon), The Party (with Peter Sellers), S. O. B., Micki + Maude, and Victor/Victoria.